Tìm giới hạn các dãy số sau, với số hạng tổng quát là:
a) $u_n=\frac{5n\sqrt n}{3n^2+n-5}                       b) u_n=\frac{2n^4-5n^2+1}{n^3+8} $
c) $u_n=\frac{n-5n^3+2}{n^2-n^3}                       d) u_n=3^n + \frac{2}{n+5} $
$e) u_n=\frac{3^{n+1}-2.5^n+14}{5^{n+2}+3^{n+2}-7}                                  f) u_n=\frac{3 \sqrt n}{2 \sqrt[]{n}+3 } (\frac{n+1}{n} )^n$
$a) 0                      b) +\infty                                 c) 5$
$d)  \lim (3^n+\frac{2}{n+5} )=\lim 3^n (1+\frac{1}{3^n}.\frac{2}{n+5})=\lim 3^n =+\infty $
e) Chia tử và mẫu cho $5^n$, ta được:    $u_n=\frac{3(\frac{3}{5} )^n-2+ \frac{14}{5^n} }{25 + (\frac{3}{5} )^n-\frac{7}{5^n} } $
Vì   $\lim (\frac{3}{5} )^n=0,   lim \frac{1}{5^n}=0 $  nên  $\lim u_n=-\frac{2}{25} $
f)  $\lim u_n=\lim \frac{3}{2+\frac{3}{\sqrt[]{n} } }.\lim(1+\frac{1}{n} )^n=\frac{3}{2}e  $

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